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Person: Carnot, Lazare Nicolas Marguérite

Lazare Carnot is best known as a geometer. In 1803 he published _Géométrie de position _ in which sensed magnitudes were first systematically used in geometry.

Mathematical Profile (Excerpt):

• Claude Carnot was a leading citizen of Nolay, a notary, judge and bailiff for the Marquisate of Nolay.
• Let us note at this point that Joseph-François-Claude Carnot became a jurist, was a member of the Court of Cessation (1801-1835), was elected to the Académie des Sciences Morales et Politiques in 1832 and became an Officer of the Légion d'Honneur.
• Claude-Marie Carnot Feulins was a soldier.
• Lazare's elementary education was first from M Masson, then from M Boisson, both excellent Latinists, at the small college in Nolay.
• Here Carnot studied mathematics, logic and theology, his teacher being Abbé Bisson.
• The Duke offered to contact the Ministry of War to allow Carnot to be admitted to the engineering corps despite recent moves to limit numbers entering.
• Carnot was taught at the School of Engineering in Mézières by Gaspard Monge among others.
• Carnot, also from Burgundy, and now an expert on fortifications had entered the Dijon Academy's competition.
• Carnot, now captain in the Corps du Royal Génie in the garrison at Arras, received two gold medals and the Academy's prize on 2 August 1784, the presentation being by the Prince of Condé himself.
• Carnot's "Éloge de Vauban" Ⓣ(Tribute to Vauban) was praised for its enthusiasm, its warmth of expression, and its compassion and he was described as learned and eloquent.
• Marc René, Marquis de Montalembert (1714-1800) had improved on Vauban's fortifications but now Carnot was quickly gaining a reputation for improving on Montalembert's ideas.
• They had three sons: Sadi Carnot, an important mathematician with a biography in this archive, was born on 19 July 1794; Nicolas Léonard Sadi Carnot was born on 1 June 1796, he became a physicist who worked on thermodynamics; and Lazare Hippolyte Carnot, born 6 April 1801, who became a journalist and then Minister of Public Instruction and a member of the Academy of Moral and Political Sciences.
• General Gratien thought this attack was too daring, so Carnot ordered his arrest right there on the battlefield.
• In September 1794, under direction from Carnot and Monge, a 'Grande École' was set up called 'École Centrale des Travaux Publics' but its name was changed to 'École Polytechnique' in the following year.
• Carnot now put into practice his military strategy which led to the French inflicting defeats on the allies.
• This highly successful military leadership led to Carnot being known as the 'Organiser of Victory'.
• A coup led by Paul Barras in 1794 led to the end of the Reign of Terror and under Carnot's influence Robespierre was removed.
• All was now not well for Carnot, however, for he strongly opposed the policies of Barras particularly when he put down a revolt of the people of Paris.
• Carnot resigned from the Committee of Public Safety because of his opposition to Barras but returned to power on 11 April 1795 when he became a member of the Directory, a five-man ruling committee.
• The year 1797 was an eventful one for Carnot.
• The book was an extended version of the essay which Carnot had submitted for the Berlin Academy Prize in 1786 but had failed to win, the prize being awarded to Simon Lhuilier.
• Thiele writes that Carnot's approach to mathematics shows strongly his engineering background.
• To Carnot negative quantities are impossible, and zero, just like infinity, is a limit.
• It is true that Weierstrass's point of view is the dominant one today; it is also true that it gives a satisfactory approach; but it is no less true that that of Carnot (who, moreover, owes a lot to Lagrange) could have given a just as satisfactory approach, and another explanation must be found for the choice ultimately made by history.
• Indeed Carnot offers a true axiomatic approach.
• Carnot became Napoleon Bonaparte's minister of war for a period of five months and was promoted further to the rank of lieutenant-general.
• Carnot's republican views made further service impossible and he retired from public life.
• Carnot is best known as a geometer.
• In this 1801 work, Carnot proposes an original idea regarding the difference between analysis and synthesis.
• Carnot's military masterpiece "De la défense des places fortes" Ⓣ(Defending strongholds) was published in 1809.
• Carnot's interests turned toward the steam engine with the first steam engine coming to Magdeburg in 1818.
• Sadi Carnot published his masterpiece on the thermodynamics of the steam engine three years later.
• Carnot was convinced that the key to organise nations and people, to elevate citizens to become true nation-builders, is based on the moral quality of leadership whose excellence is not based in the academic knowledge of theories and books, but which shows in particular under conditions of crisis, wars, and duress.
• "Circumstances develop sometimes faculties in us whose germ we did not think of, making our souls greater and giving our souls energy," Carnot said.
• That emotional quality of the mind, indispensable for overcoming obstacles and making discoveries, is what Carnot calls "enthusiasm" - passion.
• Carnot calls that creative capacity of the mind the "natural geometry," where, with a 'coup d'oeil', or glance, with "artistic ingenuity" the mind forms new hypothesis.

Born 13 May 1753, Nolay, Burgundy, France. Died 2 August 1823, Magdeburg, Prussian Saxony (now Germany).

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Tags relevant for this person:

Algebra, Group Theory

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@J-J-O'Connor

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive